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Demand theory for poverty and affluence

Miller, Anne (2022): Demand theory for poverty and affluence.

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This paper extends demand theory into the neglected area of increasing marginal utility, representing ‘deprivation’. Proposition 1 suggests that an individual’s consumption of a commodity could be represented by a bounded cardinal, S-shaped utility function. Proposition 2 indicates when to add and when to multiply utilities. Added S-shaped utilities lead to both convex- and concave-to-the-origin indifference curves, the latter space defining dysfunctional poverty. An absolute poverty line can be identified. A given commodity could potentially provide all of superior, inferior or Giffen experiences within the convex-to-the-indifference curve space. The derived structural forms, including labour supply, reveal discontinuities, envelope curves and high elasticities associated with deprivation. The two propositions together yield the familiar results of traditional neoclassical theory and provide an integrating framework for analysing utility and demand. A functional form for additive S-shaped utilities with meaningful, estimable parameters is derived in the appendix, and is used to create the diagrams.

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